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利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang(KPZ)方程、Sun-Guo-Grant(SGG)方程以及分子束外延(MBE)生长方程,并能对其进行统一的研究.研究发现,KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family-Vicsek正常标度规律;而MBE方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好.
The direct scaling analysis method is used to study the singularity index of a scale coupled with a generalized conservation law, and the singularity index of a strong-weak coupling region is obtained. As a special case, this equation includes the Kardar-Parisi-Zhang (KPZ) -Guo-Grant (SGG) equation and molecular beam epitaxy (MBE) growth equation, and can be studied uniformly.It is found that the KPZ equation and the SGG equation comply with self-imitation both in weakly coupled and strongly coupled regions And the Family-Vicsek Normal Scaling Law, while the MBE equation obeys the normal scale in the weakly coupled region and exhibits the intrinsic singular scale behavior in the strongly coupled region. The singular scale property of the growth equation obtained here is proportional to the normalized scale The theory of population, numerical simulation and experiment are in good agreement.